General feeling that West is best, as you just extend your day. But all depends on how long you are spending in each city.

I think generally in F - CX>BA>AA
With BA you want to try and pick flights with a greater probability of next gen F. I think 747/777 have similar rollout

Personally prefer the 747 over 777 with noise etc the same. You might also consider JL 787 for US to Asia (albeit only Business class), or add HKG-SIN and fly QF A380 SIN-LHR (until end March)

JFK-SFO - depends what you are after. Many on this board will try and max out the *ONE* fares so would go indirect.